Dynamic heterogeneity for the physical oncologist

Dynamic heterogeneity for the physical oncologist

Liao D, Estévez-Salmerón L and Tlsty TD 2012Conceptualizing a tool to optimize therapy based on dynamic heterogeneity* Phys. Biol. 9(6) 065005(doi:10.1088/1478-3975/9/6/065005)

Liao D, Estévez-Salmerón L and Tlsty TD 2012Generalized principles of stochasticity can be used to control dynamic heterogeneity Phys. Biol. 9(6) 065006(doi:10.1088/1478-3975/9/6/065006)

* The authors dedicate this paper to Dr Barton Kamen who inspired its initiation and enthusiastically supported its pursuit.

Dynamic heterogeneity for the physical oncologist

𝑡2 30 1

Ø

Ø

Outcome vs. frequency

Interconversion

Seeming randomness

Timings of biochemical reactions can seem to display randomness

3

Timings of biochemical reactions can seem to display randomness

4

𝑡2 3 40 1

Timings of biochemical reactions can seem to display randomness

5

𝑡2 3 40 1

𝑡2 3 40 1

Timings of biochemical reactions can seem to display randomness

6

Messy variety of durations between events Unpredictability: Varied outcomes

no protein

𝑡2 30 1

Dynamic heterogeneity for the physical oncologist

Ø

Ø

Outcome vs. frequency

Interconversion

Seeming randomness

Phenotypes can be stochastic and interconvert

8

𝑡2 3 4 5 6 7 8 90 1 10

Prot

ein

in c

ell A

Prot

ein

in c

ell B

noproduct

Relatively resistant

Relatively sensitive

Use Markov models to approximate phenotypic transitions

9

Prot

ein

in c

ell

ti

ti + Dt

𝑡2 3 4 5 6 7 8 90 1 10

Use Markov models to approximate phenotypic transitions

10

Prot

ein

in c

ell

ti

ti + Dt

cR

cSrS

rRmS

mR Ø

Ø

𝑡2 3 4 5 6 7 8 90 1 10

𝑡2 30 1

Dynamic heterogeneity for the physical oncologist

Ø

Ø

Outcome vs. frequency

Interconversion

Seeming randomness

Cell kill (t = Dt)

Cell kill (t = 0)

Metronomogram

12

Given:

Cannot directly kill “R”Illustrate: When can deplete S + R

Cell kill

Cell kill

Dt

TCD

N(0+)

N(Dt+)

N(Dt-)

Ø

Ø

𝒇 𝑺 (∆ 𝑡 )≔𝑁 (∆ 𝑡−)−𝑁 ¿ ¿

Cell kill (t = Dt)

Cell kill (t = 0)

Metronomogram

13

Given:

Cannot directly kill “R”Illustrate: When can deplete S + R

Cell kill

Cell kill

Dt

TCD

N(0+)

N(Dt+)

N(Dt-)

KilledØ

Ø

𝒇 𝑺 (∆ 𝑡 )≔𝑁 (∆ 𝑡−)−𝑁 ¿ ¿

Cell kill (t = Dt)

Cell kill (t = 0)

Metronomogram

14

Given:

Cannot directly kill “R”Illustrate: When can deplete S + R

𝒇 𝑷 (∆ 𝑡 )≔𝑁 (∆𝑡−)−𝑁 ¿¿

Cell kill

Cell kill

Dt

TCD

N(0+)

N(Dt+)

N(Dt-)

Killed

Expansion

Ø

Ø

𝒇 𝑺 (∆ 𝑡 )≔𝑁 (∆ 𝑡−)−𝑁 ¿ ¿

Cell kill (t = Dt)

Cell kill (t = 0)

Metronomogram

15

Given:

Cannot directly kill “R”Illustrate: When can deplete S + R

𝒇 𝑷 (∆ 𝑡 )≔𝑁 (∆𝑡−)−𝑁 ¿¿

Cell kill

Cell kill

Dt

TCD

N(0+)

N(Dt+)

N(Dt-)

𝑓 𝑆> 𝑓 𝑃

𝑓 𝑆< 𝑓 𝑃

𝑓 𝑆=𝑓 𝑃

1.0

0.8

0.6

0.4

0.2

0 0.2 0.4 0.6 0.8 1.0

Sens

itize

d fr

actio

n

Population expansion fraction

>Killed

Expansion

Ø

Ø

𝒇 𝑺 (∆ 𝑡 )≔𝑁 (∆ 𝑡−)−𝑁 ¿ ¿

Cell kill (t = Dt)

Cell kill (t = 0)

Metronomogram

16

Given:

Cannot directly kill “R”Illustrate: When can deplete S + R

𝒇 𝑷 (∆ 𝑡 )≔𝑁 (∆𝑡−)−𝑁 ¿¿

Cell kill

Cell kill

Dt

TCD

N(0+)

N(Dt+)

N(Dt-)

𝑓 𝑆> 𝑓 𝑃

𝑓 𝑆< 𝑓 𝑃

𝑓 𝑆=𝑓 𝑃

1.0

0.8

0.6

0.4

0.2

0 0.2 0.4 0.6 0.8 1.0

Sens

itize

d fr

actio

n

Population expansion fraction

Ø

Ø

Metronomogram

17

Given:

Cannot directly kill “R”Illustrate: When can deplete S + R

𝒇 𝑺 (∆ 𝑡 )≔𝑁 (∆ 𝑡−)−𝑁 ¿ ¿

𝒇 𝑷 (∆ 𝑡 )≔𝑁 (∆𝑡−)−𝑁 ¿¿

Dt

𝑓 𝑆> 𝑓 𝑃

𝑓 𝑆< 𝑓 𝑃

𝑓 𝑆=𝑓 𝑃

1.0

0.8

0.6

0.4

0.2

0 0.2 0.4 0.6 0.8 1.0

Sens

itize

d fr

actio

n

Population expansion fraction

S and R

R only

N(Dt+)

N(Dt-)S and R

R only

N(0+)

S and R

R only

Ø

Ø

Metronomogram

18

Given:

Cannot directly kill “R”Illustrate: When can deplete S + R

𝒇 𝑺 (∆ 𝑡 )≔𝑁 (∆ 𝑡−)−𝑁 ¿ ¿

𝒇 𝑷 (∆ 𝑡 )≔𝑁 (∆𝑡−)−𝑁 ¿¿

Dt

𝑓 𝑆> 𝑓 𝑃

𝑓 𝑆< 𝑓 𝑃

𝑓 𝑆=𝑓 𝑃

1.0

0.8

0.6

0.4

0.2

0 0.2 0.4 0.6 0.8 1.0

Sens

itize

d fr

actio

n

Population expansion fraction

S and R

R only

N(Dt+)

N(Dt-)S and R

R only

N(0+)

S and R

R only

Ø

Ø

Metronomogram

19

Given:

Cannot directly kill “R”Illustrate: When can deplete S + R

𝒇 𝑺 (∆ 𝑡 )≔𝑁 (∆ 𝑡−)−𝑁 ¿ ¿

𝒇 𝑷 (∆ 𝑡 )≔𝑁 (∆𝑡−)−𝑁 ¿¿

Cell kill

Cell kill (t = 0)

Cell kill (t = Dt)

Cell kill

Expansion andinterconversion

Dt

TCD

N(0+)

N(Dt+)

N(Dt-)

𝑓 𝑆> 𝑓 𝑃

𝑓 𝑆< 𝑓 𝑃

𝑓 𝑆=𝑓 𝑃

1.0

0.8

0.6

0.4

0.2

0 0.2 0.4 0.6 0.8 1.0

Sens

itize

d fr

actio

n

Population expansion fraction

Ø

Ø

𝑡2 30 1

Dynamic heterogeneity for the physical oncologist

Ø

Ø

Outcome vs. frequency

Interconversion

Seeming randomness

Dynamic heterogeneity for the physical oncologist

Liao D, Estévez-Salmerón L and Tlsty TD 2012Conceptualizing a tool to optimize therapy based on dynamic heterogeneity* Phys. Biol. 9(6) 065005(doi:10.1088/1478-3975/9/6/065005)

Liao D, Estévez-Salmerón L and Tlsty TD 2012Generalized principles of stochasticity can be used to control dynamic heterogeneity Phys. Biol. 9(6) 065006(doi:10.1088/1478-3975/9/6/065006)

* The authors dedicate this paper to Dr Barton Kamen who inspired its initiation and enthusiastically supported its pursuit.